You are highly unlikely to find "cheap" eats or anything else near tourist sites anywhere in the world. Expensive and not very good is more their style.
It is possible to eat relatively cheaply in London, by eating like the locals do. At noon follow office workers to see where they eat. It may not be gourmet, but despite all the rumours and lies, the British are not all gastronomic idiots.
Shopping areas sometimes have reasonably cheap restaurants, although that is under threat from the plague of chain coffee shops etc infesting the world.
Universities and colleges often have reasonably priced restaurant facilities open to the public. Students unions also often have cheap but surprisingly good canteens, although some require ID in the evenings.
Pubs (some) offer good to excellent food at good prices.
Many more upmarket restaurants have surprisingly cheap lunch or "pre-theater" menus. Often a fraction of their full evening service.
I no longer live in London so I'm not recommending anywhere specific but, as you don't like Indian much, how about Chinese, Greek, Caribbean, and literally dozens of other "ethnic" choices.
If I were you, I'd be reading as many on-line restaurant reviews as possible. For local reviews, I recommend Time Out or the Evening Standard (terrible newspaper, but sound on London eating) or the Guardian/Observer sites.
